I was climbing at Rumney last weekend and I encountered quite a number of bolts with loose hangars, that is bolts where the hangar was loose to spin, and even in some cases where the nut hold the hangar on the bolt was loose enough to be turned with my fingers. How safe/unsafe are such bolts? Can they just be tightened up? Should I take to climbing with a wrench?

You can just tighten them up but make sure you look to see if there is any rusting or other reasons for them to be loose. When you do tighten them make sure not to over tighten. A good rule of thumb is when the nut is sung, tighten 1/4 of a turn, Yes this is not a hard a fast rule and not tighting them by the book, but who takes a torque wrench with them.

Unsafe or not depends on what type of bolt they are, wedge (thru) bolts are just as good when they are loose, multi-piece decidly worrying. Why there are so many loose is the big question, an occassional spinner can be expected but more than that implies the bolts are too small and are generally moving, this really ought to be checked out by someone with a lot of experience and preferably a tester. The DMM nutkey has a hex hole for 10mm bolts so 17mm, Grivel do one with 13mm,17mm and 19mm. Both are pretty marginal for properly tightening bolts and won´t fit US sizes anyway.

I was climbing at Rumney last weekend and I encountered quite a number of bolts with loose hangars, that is bolts where the hangar was loose to spin, and even in some cases where the nut hold the hangar on the bolt was loose enough to be turned with my fingers. How safe/unsafe are such bolts? Can they just be tightened up? Should I take to climbing with a wrench?

Unfortunately this is a complicated question and the correct answer can only be provided on a case by case study. However, the general rule of thumb is if only the hanger is loose, it is probably safe. However, if the bolt moves, it may not be safe, especially if it is a glue-in bolt. If the nut on a wedge bolt is loose, but the stud itself is not, just tighten the nut and move on, it is likely safe. But again, if the bolt itself ever moves, don't trust it!